Related papers: A Coupling for Triple Stochastic Integrals

This work proposes a sampling-based (non-intrusive) approach within the context of low-rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with…

We derive the optimal rate of convergence for the mean squared error at the terminal point for anticipating linear stochastic differential equations, where the integral is interpreted in Skorohod sense. Although alternative proof techniques…

For the approximation and simulation of twofold iterated stochastic integrals and the corresponding L\'{e}vy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very…

The problem of the construction of strong approximations with a given order of convergence for jump-diffusion equations is studied. General approximation schemes are constructed for L\'evy type stochastic differential equation. In…

Higher order schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we propose a derivative-free Milstein type scheme to approximate…

This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…

For stochastic approximation algorithms with discontinuous dynamics, it is shown that under suitable distributional assumptions, the interpolated iterates track a Fillipov solution of the limiting differential inclusion. In addition, we…

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…

The article is devoted to the mean-square approximation of iterated Ito and Stratonovich stochastic integrals in the context of the numerical integration of Ito stochastic differential equations. The expansion of iterated Ito stochastic…

Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled…

This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…

We provide convergence rates for space approximations of semi-linear stochastic differential equations with multiplicative noise in a Hilbert space. The space approximations we consider are spectral Galerkin and finite elements, and the…

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…

We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein's weak error analysis on the one-step approximation of…

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by $N$ random variables. The random…

A finite element solution coupled with an interior penalty discontinuous Galerkin solution are defined for the approximation of the coupled 3D-1D solute transport problem. Under sufficient regularity for the weak solutions, optimal error…

Given a stochastic differential equation (SDE) in $\mathbb{R}^n$ whose solution is constrained to lie in some manifold $M \subset \mathbb{R}^n$, we propose a class of numerical schemes for the SDE whose iterates remain close to $M$ to high…

We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…

We consider certain systems of three linked simultaneous diagonal equations in ten variables with total degree exceeding five. By means of a complification argument, we obtain an asymptotic formula for the number of integral solutions of…

A direct three dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering…